A350295 2nd subdiagonal of the triangle A350292.

6, 8, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 171, 190, 210, 231, 253, 276, 300, 325, 351, 378, 406, 435, 465, 496, 528, 561, 595, 630, 666, 703, 741, 780, 820, 861, 903, 946, 990, 1035, 1081, 1128, 1176, 1225, 1275, 1326, 1378, 1431, 1485, 1540

Offset

3,1

Links

Harvey P. Dale, Table of n, a(n) for n = 3..1000

Heiko Harborth and Hauke Nienborg, Saturated vertex Turán numbers for cube graphs, Congr. Num. 208 (2011), 183-188.

Mathonline, Cube Graphs

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

a(n) = binomial(n, 2) = A000217(n-1) for n > 4 with a(3) = 6 and a(4) = 8 (see Theorem 3 in Harborth and Nienborg).

O.g.f.: x^3*(2*x^4 - 3*x^3 - 4*x^2 + 10*x - 6)/(x - 1)^3.

E.g.f.: x^2*(x^2 + 6*x + 6*exp(x) - 6)/12.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 7.

Mathematica

Join[{6, 8}, Table[Binomial[n, 2], {n, 5, 56}]]
LinearRecurrence[{3, -3, 1}, {6, 8, 10, 15, 21}, 60] (* Harvey P. Dale, Jul 01 2022 *)

Crossrefs

Cf. A000217, A112355, A161680, A350292.

Sequence in context: A048886 A349477 A161545 * A165583 A229965 A165473

Adjacent sequences: A350292 A350293 A350294 * A350296 A350297 A350298

Keyword

nonn,easy

Author

Stefano Spezia, Dec 23 2021

Status

approved